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SSSSS [86.1K]
3 years ago
5

(a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the out

comes equally likely? 1, 2, 3, 4, 5, 6; not equally likely 1, 2, 3, 4, 5, 6; equally likely 0, 1, 2, 3, 4, 5, 6; not equally likely 0, 1, 2, 3, 4, 5, 6; equally likely
Mathematics
1 answer:
Ne4ueva [31]3 years ago
8 0

Answer:

Sample space: {1,2,3,4,5,6}

All equally likely to occur

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Let x,y be the dimensions of the rectangle. We know the equations for both area and perimeter:

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\begin{cases}xy=36\\x+y=18\end{cases}

From the second equation, we can deduce

y=18-x

Plug this in the first equation to get

xy=x(18-x)=-x^2+18=36

Refactor as

x^2-18x+36=0

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x=9\pm3\sqrt{5}

Both solutions are feasible, because they're both positive.

If we chose the positive solution, we have

x=9+3\sqrt{5} \implies y=18-x=18-9-3\sqrt{5}=9-3\sqrt{5}

If we choose the negative solution, we have

x=9-3\sqrt{5} \implies y=18-x=18-9+3\sqrt{5}=9+3\sqrt{5}

So, we're just swapping the role of x and y. The two dimensions of the rectangle are 9+3\sqrt{5} and 9-3\sqrt{5}

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Answer:

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